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Daniel P. Snowman

Publications and source records attributed to Daniel P. Snowman.

5 recordsLinked to original sources
arXiv2024

The effects of Repulsive Biquadratic Interactions in a Blume-Emery-Griffiths Spin-Glass with Competing, Attractive Biquadratic Cross-link Interactions

A BEG Hamiltonian is used to model an Ising spin glass with annealed vacancies on a hierarchical lattice. In addition to competing bilinear interactions, repulsive biquadratic interactions on the perimeter of our unit structures compete with attractive cross-link interactions. Ordering and transitions in this system are probed by generating several phase diagrams, using renormalization group methods, for a range of constant K/J. A physical interpretation is offered for each sink corresponding to a bulk phase in phase space and critical exponents are calculated for the higher-order transitions.

cond-mat.stat-mech↗
arXiv2009

A Dilute Ising Ferromagnet on a Hierarchical Lattice with Attractive Biquadratic Interactions

This paper considers a dilute Ising ferromangnet with annealed vacancies and attractive biquadratic interactions. Phase diagrams have been calculated while varying the temperature and concentration of annealed vacancies in the system while maintaining constant, attractive biquadratic couplings. These results have been produced using renormalization group analysis with a hierarchical lattice. Critical exponents have been calculated and each basin of attraction interpreted.

cond-mat.stat-mech↗
arXiv2009

A Blume-Capel Ising Ferromagnet with Annealed Vacancies on a Hierarchical Lattice

A dilute Ising ferromagnet is considered in this study using renormalization group techniques with a hierarchical lattice. A series of phase diagrams have been produced that probe the effects of varying the temperature and concentration of nonmagnetic impurities. Each phase diagram corresponds to a different strength for the internal coupling coefficients on our lattice. Phases have been interpreted and critical exponents calculated for the higher order transitions.

cond-mat.stat-mech↗
arXiv2007

Geometric Frustration and Interparticle Gap Size Distributions in Ordered Hexagonal Polydisperse Disk Packs

This work analyzes the distribution and size of interparticle gaps arising in an ensemble of hexagonal unit structures in the xy plane when packing disks with a Gaussian distribution of radii with mean (r) and standard deviation $Δr$. During the course of this investigation an equivalency is established between gaps arising in hexagonal unit structure packs and nine-ball billiard rack patterns. An analytic expression is derived for the probability distribution and location of interparticle gaps of magnitude $Γ$. Due to the number of variables and large number of possible arrangements, a Monte Carlo simulation has been conducted to complement and probe the analytic form for three very different systems: i) billiard balls with Billiard Congress of America (BCA) specifications, ii) US pennies with specifications of the US Mint, and iii) a hypothetical system with $r = 1.0 m$ and $Δr = 1x10^{-10}$ m corresponding to the scale of one atomic radius. In each case, probability density distributions of gap sizes have been calculated for those $Δr$ above, and also for 2$Δr$ and 0.5$Δr$, respectively. A general result is presented for the probability of a nonzero normalized ($\fracΓ{Δr}$) gap size arising, $P(Γ\geq αΔr)= 1-0.124α$, where $α$ is a constant $\leq 5.0$. This curious result reflects the phenomenon of geometric frustration; the inability of the system to simultaneously satisfy all geometric constraints required by a perfect-rack sans interparticle gaps.

cond-mat.stat-mech↗